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A merchant has $1000$ kg of sugar, part of which he sells at $8 %$ profit and the rest at $18 %$ profit. He gains $14 %$ on the whole. The quantity of sugar sold at $18 %$ profit is

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560

600

400

640

answer is B.

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Detailed Solution

Given that a merchant has

1000

kg of sugar, part of which he sells at

8 %

profit and the rest at

18 %

profit. He gains

14 %

on the whole.
Let the C.P. of sugar be Rs.

x

per kg.
Then, C.P. of 1000 kg of sugar

=

Rs. 1

000 x

Let the sugar sold at

8 %

gain by

y

kg. (C.P. of y kg = xy)
Then, sugar sold at

18 %

gain

= (1000 - y)

kg (C.P. of y kg = x(1000-y))
∴ S.P. of y kg + S.P.of (1000 - y) kg = S.P. at 14% profit

∴ (\frac{108}{100} \times xy) + [\frac{118}{100} \times x (1000 - y)] = \frac{114}{100} \times 1000 x

\Rightarrow \frac{108 y}{100} + 1180 - \frac{118 y}{100} = 1140

\Rightarrow \frac{10 y}{100} = 40

\Rightarrow y = 400

∴

Quantity sold at 18% gain

= (1000 - 400)

\Rightarrow

Quantity

= 600

kg.
Thus, the quantity of sugar sold at 18% profit is 600kg.
Therefore, the correct option is 2.

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